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Will a scrambled picture ever come back? Arnold's cat map shears a picture, cuts what sticks out and slides it back, again and again. The picture is 199 × 199 cells, 39,601 in all. Each step moves every cell by (x, y) → (2x + y, x + y), wrapped mod 199. It goes to streaks, then grain, then streaks again, and on step 11 every cell is home. The matrix [[2,1],[1,1]] has determinant 1, so cells only move, never merge, and finitely many cells must return. 11 is this grid's count: 150 × 150 takes 300. Source: Wikipedia, «Arnold's cat map». Simplified: a real cut rubber sheet would keep its cuts and never come back whole. No voice, no music. #linearalgebra #catmap #matrix

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